The integrated computing system optical network has been viewed as a promising platform to support real-time distributed computing applications. For such a system involving so many heterogeneous computing and network resources, faults seem to be inevitable. Therefore, a fault-tolerant scheme is necessary to improve the availability of the integrated system. However, existing joint task scheduling schemes for real-time distributed computing applications generally do not consider the application availability issues when making scheduling decisions. In this paper, we develop an availability-aware joint task scheduling (AAJTS) scheme, by both taking into account availability improvement and timing requirements. The proposed scheme iteratively enhances the application availability under deadline constraint to protect data communication tasks from network link failures. Extensive simulations demonstrate the effectiveness and the feasibility of the proposed scheme.